I guess you want soon also more complex forms than simple arc. This answer covers them.
Modern Illustrator could use your brush stroke PNG image as a brush - draw a curve with the Pen or other path making tool and apply your brush and that's that. Unfortunately legacy Illustrator doesn't accept such attempt with bitmap images, only vector shapes work as brush there.
I do not recommend as the first option tracing your PNG to vector because accurate enough look needs easily hundreds of small paths (=thousands of anchor points) which pull your computer on its knees if you want to paint something complex with that brush.
Test how good result your system can carry without slowing down too much. A few separate curves can well work ok, but painting with them can soon become very sluggish. See a tracing attempt in the end of this story.
There's available Envelope distortion which also can warp your PNG to the wanted geometric form. I recommend you it as the 1st option to test. An example:
This is your bush stroke clipped from your screenshot. In the next image it's imported to Illustrator and Object > Envelope Distortion > Make with Top Object is applied. The top object is the black closed path which can be quite random. But it must be a closed path:
Note that the empty area between the red stroke and the bounding box of the image take also their part of the room inside the envelope.
Read CS4 Illustrator's manual to read other envelope distortion options than Make with Top Object. A simple arc warping delivers what you asked in the question. Several simple warping options are also available in Photoshop.
Tracing and using as brush:
Here the brush stroke is traced to vector and the result (=about 3600 anchor points) is dragged to the Brushes collection and defined to be an art brush:
The brush is applied to a random path in the right. As a single path it doesn't degrade the apparent performance, but having them say 100 probably causes something noticeable. After having actually 128 copies In my old machine zooming and drawing something new started with about 0,5 seconds long pause.